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Level III

Regression using absoulte residuals

I have yearly precipitation extremes data (data in frequency, 0 to 15) from 1989 to 2019. My hypothesis is that climate extremes (precipitation) increased in last 16 years (2004 to 2019) than previous 15 years (1980 to 2003).

I have performed regression with this data and my results show that the regression line is downward. Then I performed regression using the absolute residuals and this time the results show that regression line of the absolute residuals is upward.

Am I doing right?

Why two kinds of results?

Which one is right?

2 ACCEPTED SOLUTIONS

Accepted Solutions
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Staff

Re: Regression using absoulte residuals

First of all, why not enter your questions directly instead of putting them into an Excel workbook that we must open?

Second, there is not JMP data table. I could make one from the columns in the Excel workbook, but you do not seem to be using JMP. This Discussion forum is for JMP users.

Here is my answer to your questions.

1. Use of permutation test. I already answered this question previously.
2. Use of 'absolute' regression for non-normal data. I already answered this question previously.
3. Compare spread of two periods of time. I already answered this question previously.
4. Suggest another method. I already answered this question previously.

We seem to be 'going around in circles.'

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Level III

Re: Regression using absoulte residuals

Mark,

Thanks for your reply. I use JMP on a regular basis. Sorry, my mistake that I forgot to attach JMP file. I have attached it now that shows that I do use it

The dept. I work with have three licenses/users and they are frequent users.

21 REPLIES 21
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Staff

Re: Regression using absoulte residuals

I am not sure that linear regression is the correct method to compare two time periods. Regression requires matching a X and Y value, like Precipitation versus Year for a trend. What is your response and what is your regressor?

How did you perform both regressions in JMP? Knowing the methods that you used will aid us in helping your with a correct answer.

If you are using counts as a response, then a Poisson loglinear regression might be more satisfactory. But I still don't see how you compared the two time periods. Just by comparing the parameter estimates? If so, there are more comprehensive methods for such a case. Assuming that the trend is linear over time, then you might have a linear predictor like Precipitation = constant + beta(1)*Year + beta(Period) + beta(2)*Period*Year. This way, you can test if there is an average difference between the two periods and if the trend is different between the two periods.

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Level III

Re: Regression using absoulte residuals

Hi Mark,

Thanks so much. I have added a excel file which will show you how I have analyzed the data. Your answer will be highly appreciated.

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Staff

Re: Regression using absoulte residuals

1. You are comparing counts of occurrences of extreme precipitation during two periods of time. The permutation test is a good way to consider the observed difference.
2. A permutation test or ANOVA should answer your question. Other non-parametric tests are valid if you are concerned about any difference between the two periods.
3. The simple linear regression is testing if the mean response depends on the predictor Year.
1. The trend is not significant because the apparent increase in occurrences over time is not unusual while assuming that there is no trend.
2. The regression of the abs(residuals) versus the original counts is a completely different analysis. You cannot compare the two regressions.
3. The second regression indicates that your response might be homoscedastic. There is not a mean trend, there is a variation trend.
4. Yes, the permutation test is appropriate for a simple comparison of the two periods.
1. The statement based on the one-sided permutation test (counts are greater in the second period) is simply that it is estimated that 15% of samples had a difference at least as large as the observed difference.
2. Where did the operational definition for counting come from? That is occurrence of more than 40 mm rain in 4 consecutive days.

I ran my own permutation test with the data that you supplied. I consistently get a different result. Here is one of them:

So my one-sided p-value would be 1185 / 2501 = 0.4738. That is, it is estimated that 47% of the samples produce a difference at least as large as the observed difference assuming the null hypothesis is no difference (basis for permutations).

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Level III

Re: Regression using absoulte residuals

Hi Mark,

Thank you so much for your kind support and advise. The info you provided is very useful. I have done a couple of analyses and looking for some additional advise. Pleased see the attached file. I would appreciate your advsie. Regards

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Staff

Re: Regression using absoulte residuals

Your residual analysis indicates that the log Y is better suited to the regression because the variance is now constant. Do you know about the built-in Box-Cox transformation? This automated procedure is a generalization of the ad hoc power transformations. The spectrum of parameter values includes the log. A Box-Cox transformation parameter equal to zero is the same as the log. Now when I say the same, this transform does not yield the same value as the log or the power, but they may be interpreted as such. So a parameter value of 2 is interpreted as the square of Y and a value of -1 is interpreted as the reciprocal.

Caution: your wording (thinking) is a bit dangerous. I would not say that there is "no evidence" when the p-value is not below some subjectively chosen threshold (ɑ). I would say that there is insufficient evidence that I would reject the null hypothesis in the test.

Anyway, glad that you are able to progress with your analysis.

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Level III

Re: Regression using absoulte residuals

Hi Mark,
Thanks so much for your support.
I just tried the Box Cox transformation, and gotten an error "Cannot do Box-Cox because of negative or zero Y value 0".
Can you please advise. Additionally, I wanted to make it sure that I apply Box Cox transformation on the original frequency data and not on residual.
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Staff

Re: Regression using absoulte residuals

Yes, I meant transform the original response. I forgot that you have some count = 0, so this approach won't work. It was just an alternate idea.

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Level III

Re: Regression using absoulte residuals

Hi Mark,

I performed the permutation test again a few times. Please see the attached file. My results are totall different than yours, means, I am doing a mistake. I run permutation while I think you did bootstarap. Please advise.

Before I contacted you a Mathematics Prof suggsted me  using permutation than bootstrap. Therefore I used  permutationt. Also, I do not have an access of Bootstarap.

Also, how you got value of 1185 / 2501 = 0.4738.

Regards

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Staff

Re: Regression using absoulte residuals

My result of 1185 / 2501 = 0.4738 is from 1185 samples out of 2501 total bootstrapped samples exhibited a difference greater than your observed difference.

JMP does not perform the permutation test as far as I know. How did you perform this test with JMP?

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